The major bottleneck of quantum molecular dynamics is the calculations of electronic states and their derivatives. Quantum computers are supposed to revolutionize the electronic structure problems of quantum chemistry by leveraging quantum systems for computation. Due to the noise of quantum hardware, the variational quantum eigensolver (VQE) is proposed accordingly. However, the VQE-type methods suffer from optimization problems, and most of the current VQE algorithms only focus on the ground state. To overcome these obstacles, we developed an efficient quantum Krylov subspace algorithm by leveraging the iterative growth of Krylov subspace. Such subspace methods remove the optimization problems suffered in the VQE-type of methods. The newly proposed quantum Krylov subspace algorithm is employed to study the excited-state properties of various systems on both simulators and quantum devices. In addition, based on the quantum algorithms for excited states, we developed a framework to measure the non-adiabatic couplings between different electronic states. Consequently, a hybrid quantum-classical algorithms for non-adiabatic molecular dynamics id developed. We believe that our recent developments provide a feasible tool for studying excited-state and non-adiabatic phenomena on quantum computers.

Non-adiabatic molecular dynamics: Quantum kyrlov subspace method for excited states and non-adiabatic couplings

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